Binary Level Set Method for Topology Optimization of Variational Inequalities

摘要

The paper is concerned with the topology optimization of the elliptic variational inequalities using the level set approach. The standard level set method is based on the description of the domain boundary as an isocountour of a scalar function of a higher dimensionality. The evolution of this boundary is governed by Hamilton-Jacobi equation. In the paper a binary level set method is used to represent sub-domains rather than the standard method. The binary level set function takes at convergence value 1 in each sub domain of a whole design domain and -1 outside this sub domain. The sub domains interfaces are represented by discontinuities of these functions. Using a two-phase approximation and a binary level set approach the original structural optimization problem is reformulated as an equivalent constrained optimization problem in terms of this level set function. Necessary optimality condition is formulated. Numerical examples are provided and discussed.